Cone
Details and Options
- Cone can be used as a geometric region and a graphics primitive.
- Cone [] is equivalent to Cone [{{0,0,-1},{0,0,1}}].
- Cone represents a filled cone region where and the vectors are orthogonal with TemplateBox[{{v, _, 1}}, Norm]=TemplateBox[{{v, _, 2}}, Norm]=1, and and .
- Cone can be used in Graphics3D .
- In graphics, the points pi and radii r can be Scaled and Dynamic expressions.
- Graphics rendering is affected by directives such as EdgeForm , FaceForm , Specularity , Opacity , and color.
- Cone [{spec1,spec2,…},{r1,r2,…}] represents a collection of cones with specifications speci and base radii ri.
Examples
open all close allBasic Examples (4)
A unit radius and two units height cone:
A cone from the origin to {1,1,1} with radius 1/2 at its base:
Differently styled cones:
Volume and centroid:
Scope (22)
Graphics (12)
Specification (5)
If no radius is specified, it is assumed to be 1:
Cone with different radii:
Cone with different directions:
Short form for a cone centered at the origin with a base radius 1:
Multiple cones:
Styling (5)
Color directives specify the face colors of cones:
FaceForm and EdgeForm can be used to specify the styles of the faces and edges:
Different properties can be specified for the front and back faces using FaceForm :
Cones with different specular exponents:
White cone that glows red:
Opacity specifies the face opacity:
Regions (10)
Embedding dimension is the dimension of the space in which the cone lives:
Geometric dimension is the dimension of the shape itself:
Membership testing:
Get conditions for membership:
Volume:
Centroid:
Distance from a point:
The equidistance contours for a cone:
Signed distance from a point:
Nearest point in the region:
Nearest points to an enclosing sphere:
A cone is bounded:
Find its range:
Integrate over a cone region:
Optimize over a cone region:
Solve equations in a cone region:
Applications (5)
Find the minimum surface area for a cone with volume :
Compare with some other cones of the same volume:
Define a region by the intersection of a cone and a plane:
Visualize the intersection:
A simple 3D arrow chart:
Define a ChartElementFunction based on Cone :
BarChart3D uses Cone to produce 3D bar charts:
Histogram3D can similarly use Cone :
Use Cone to display bubbles in BubbleChart3D :
Properties & Relations (6)
Use Scale to get an elliptical cone:
Cone is used as a 3D arrowhead in Arrow :
Cone is a special case of Tube :
Get a truncated cone by specifying different radii in Tube :
A parametric specification of a cone shell generated using ParametricPlot3D :
An implicit specification of a cone shell generated by ContourPlot3D :
ImplicitRegion can represent any Cone region:
Neat Examples (3)
Random unit cones:
Sweep a cone around an axis:
Nested transparent cones:
See Also
Related Guides
Text
Wolfram Research (2008), Cone, Wolfram Language function, https://reference.wolfram.com/language/ref/Cone.html (updated 2014).
CMS
Wolfram Language. 2008. "Cone." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2014. https://reference.wolfram.com/language/ref/Cone.html.
APA
Wolfram Language. (2008). Cone. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Cone.html
BibTeX
@misc{reference.wolfram_2025_cone, author="Wolfram Research", title="{Cone}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/Cone.html}", note=[Accessed: 04-January-2026]}
BibLaTeX
@online{reference.wolfram_2025_cone, organization={Wolfram Research}, title={Cone}, year={2014}, url={https://reference.wolfram.com/language/ref/Cone.html}, note=[Accessed: 04-January-2026]}